Finding all monomials in a polynomial ideal

Abstract

Given a $d\times n$ integer matrix $A$, the main result is an elementary, simple-to-state algorithm that finds the largest $A$-graded ideal contained in any ideal $I$ in a polynomial ring $\mathbb{k}[x_1,\dots ,x_n]$. The special case where $A$ is an identity matrix yields that $(t.I)\cap \mathbb{k}[x_1,\dots ,x_n]$ is the largest monomial ideal in $I$, where the generators of $t.I$ are those of $I$ but with each variable $x_i$ replaced by $t_i{x}_i$ for an invertible variable $t_i$.

2 pages

Cited by in corpus (2)

• Computing elements of certain form in ideals to prove properties of operators
• Mono: an algebraic study of torus closures